No 159: Volatility of the Stochastic Discount Factor, and the Distinction between Risk-Neutral and Objective Probability Measures

Gurdip Bakshi (), Zhiwu Chen () and Erik Hjalmarsson ()

Abstract: This paper derives a measure that characterizes the
distance between the risk-neutral and the objective probability measures
for any candidate asset pricing model. We formally show that the distance
metric is equal to the volatility of the stochastic discount factor. This
theoretical result gives an alternative interpretation to the
Hansen-Jagannathan bounds: they provide a lower bound for the distance
between the objective and the risk-neutral probability measures. Our
empirical application provides support for the notion that the crash of
1987 has widened the wedge between the risk-neutral and the objective
probability measures.

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